An alternative numerical approach for an improved ecological model of interconnected lakes with a fixed pollutant

There is currently an undeniable demand for solutions to environmental issues, especially water pollution. Water is essential for life and lakes constitute a big portion of water sources. In this study, we introduce a modified numerical approach to a dynamic ecological model focused on a lake pollution problem. The model includes three connected lakes with certain parameters and unknown functions such as pollution quantities and lake volumes. First, a preliminary mathematical analysis of the variables of each lake is presented taking into account the system components and parameters. Then, we present our numerical approach considering a series expansion to approximate the problem with the help of the truncated Taylor series. We describe a convergent technique, and finally, demonstrate the numerical simulations of the approach for the different unknowns with appropriate parameters. According to the results, the application of our alternative approach to the lake pollution problem is successful in terms of producing highly accurate information outputs about pollutant quantities a better approximation than the previously studied numerical approaches for the unknown functions of time. Furthermore, it is applicable to other similar ecological and environmental dynamic systems, and to related fields.